Geometry, which was long considered the most elegant and irrefutable of the sciences, was dealt the last of a series of deadly blows last week with the unveiling of a five year archeological dig.

“The age of Euclid is over” said Wermer Heisenstat, referring to the famous geometrical theorist whose work was once required reading for every elementary school pupil, “While his model has been very much under fire for most of the last few years, we have finally found the definitive evidence in the fossil record.”

Theorists have long called into question the progression of Euclid’s most well known text Elements, though it was not until recently that scientists began to call into question the trigonocentric- that is, triangle based- nature of Euclid’s various proofs, a critique that was originally put forth in Erhard Schroeder’s now famous work The Two Missing Sides of Euclid’s Triangle.

“Euclid essentially treats the triangle as distinct from other shapes” explains Harvard’s John Benson, “In Euclid, there is a bright line distinguishing the triangle from the pentagon, for example. This naturally lead to a kind of divinization of the triangle, which explains why it was featured as such a prominent part of medieval cathedrals. In light of the new evidence, however, we can see that older distinction as a somewhat naive mistake, one that we can now definitively correct using the fossil record.”

scholars have long disputed the natural basis of geometry, but until now the debate lacked the sort of hard evidence that could silence a dwindling body of theorists that held to the natural priority of the triangle model in geometric theorems. The debate centered around Euclid’s foundational belief that the triangle was the basis for the generation of the pentagon. “Euclid treats the pentagon as essentially an afterthought to the triangle” Benson explains, “If anyone looks for the pentagon in the Elements he or she will have to go through half the book before Euclid even mentions it. The new evidence suggests that Euclid is progressing in exactly the wrong way, since pentagonal shapes are found 35 million years before triangular shapes in the fossil record.”

The release of the evidence was met with a firestorm of controversy. Harvey Longman, a senior research fellow at the Aleithia Institute, took issue with the dating of the fossils: “there is simply no way to accurately parse the strata of late chronolithic sediments” he said, and then quickly added “the evidence is pretty convincing, I must admit, but we can’t forget the teaching value of Euclid, who still provides a pretty good model for the distinction of shapes, even if it is ultimately not entirely in line with natural history.”

In spite of the tremendous success of the newer pentagonal theorems among the archeologists, there was a note of reflection and regret. “We have all gotten used to assigning a certain priority to the triangle, and we have grown to see it as a sort of separate, distinct, and wholly autonomous shape” said Schroeder. “But we can no longer accept the sort of exalted position that the triangle has. It is, in the end, only a sort of warped pentagon, a shape which proceeded out of a random selective process progressing over 30 to 40 million years.”

“There is a part of us that is sad to see Euclid go” said Schroeder “But that is simply the way science is. Upheavals are what makes the study of any science so satisfying to participate in.”

I call them “two parts” although it is not clear to me if they are really two different accounts.

1) Happiness can mean a feeling of well being, contentment, satisfaction, etc.

2) Happiness can mean something that is self-evidently desirable- this meaning seems to be at work insofar as no one ever asks someone “why they want to be happy”.

If happiness only means contentment, satisfaction, etc. then it is possible that one could question whether happiness is even worth having- who cares if Pol Pot was content with his life? He may very well have been, he may very well have scored a perfect 10 on any statistical analysis of happiness. But it is a dark or perverse mind that is content with itself in spite of its wickedness. It may well be the case that all those who we despise might lead lives they are mostly satisfied with- and at least in this sense they are happy.

If we are open to the possibility that at least some kinds of happiness is not worth having, then we can see #1 above as one complete account of happiness. If we cannot do this, then we cannot separate happiness from human morality- regardless of what account we give of it. Along with Socrates, we must say that Tyrants, Felons, and immoral people can never be happy, regardless of how content they are with their lives.

…I have been deceived many times by my own words, spoken both in French and in Latin. I have sometimes thought that a word meant one thing, when in fact it meant another, and I have often times misspelled words and been completely unaware of my error. I therefore will treat all languages as uncertain and totally false. I will forget the meaning of every term, and never speak again.

Consider all material things as contained in an underground cave. One day, with a great upheaval of the earth, a fissure crack opens up in the roof of the cave, and the whole cave is flooded with light and the vision of the whole universe.

The the fissure in the roof is man. Considered in himself, he is a void, a gap, an utter nullity. Considered in relation to the universe that he makes visible, he is infinite and without limits.

Anything in the cave would hold the fissure to be the greatest and most lofty feature of the cave, not because it is a crack, but rather because it is a principle by which the universe became known.